EECS4422/5323 Computer Vision, Fall 2021
Theory Assignment 1
You have 48 hours to complete this assignment; there are absolutely no extensions. Answer the
questions in the spaces provided on the question sheets; scan and submit your completed
assignment. No questions are allowed, such emails will be ignored. If in doubt, state your
assumption clearly. You are only allowed the aid of the course lecture slides and assigned textbook
readings. There is absolutely no communication allowed among students about this assignment.
Any collusion among students or usage of forbidden aids found will be considered an
academic integrity offence and will be dealt with accordingly.
Student name:
Student number:
Question Your Mark Maximum Mark
1 1
2 1
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5 1
6 1
7 5
8 5
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10 5
11 2
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Total 35
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1. [1 point] (Circle all appropriate answers) Which of the following factors is not an extrinsic or intrinsic parameter
of the perspective projection camera model?
(a) lens thickness
(b) focal length
(c) offset of optical centre
(d) image resolution
(e) exposure
(f) pinhole size
(g) the transformation between the world to camera frame
(h) time of day
2. [1 point] (Circle all appropriate answers) A homography can represent the following transformations
(a) rotation
(b) scaling
(c) translation
(d) any transformation you can think of, to quote Steve Jobs a homography is “magical”
(e) none of the above
3. [1 point] (Circle all appropriate answers) All vanishing points
(a) map within the image frame
(b) always appear within the image frame
(c) converge to a finite point
(d) are shared by parallel lines that are strictly coplanar in the world
(e) none of the above
4. [1 point] (Circle all appropriate answers) The vanishing points can change with
(a) scene brightness
(b) camera translation
(c) camera rotation
(d) none of the above
5. [1 point] (Circle all appropriate answers) The orthographic projection model considers the
(a) the camera focal length
(b) the depths of the scene point
(c) the lens thickness
(d) none of the above
6. [1 point] (Circle all appropriate answers) If you take a picture, rotate the camera about its origin and take a
second picture, the transformation between points that can be observed in both views is a function of the
(a) the camera focal length
(b) the camera aperture size
(c) the intrinsic camera parameters
(d) the extrinsic camera parameters
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(e) the depth of the scene points
(f) none of the above
7. [5 points] Assume the imaging process is modelled with a thin lens; the focal length is 2cm. The image plane
is placed 100cm from the lens. At what distance (in cm) should a point in the world be located from the lens so
that the image of the point is in perfect focus? Show all your work.
8. [5 points] The orthographic projection of two parallel lines in the world (i.e., 3D lines) are parallel lines in the
image. Show a proof justifying your answer.
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9. [5 points] A scene point at coordinates (X,Y,Z) = (200, 300,−1975) in the world is perspectively projected
into an image at coordinates (x, y) = (−20,−30), where both coordinates are given in millimeters in the camera
coordinate frame and the camera’s principal point is at coordinates (0, 0, f ). The camera reference frame is
translated 843 mm in the negative direction along the z-axis relative to the world reference frame. What are
values for the camera intrinsics and extrinsics? Show all your work.
10. [5 points] In class we discussed the dolly zoom that was first used in Alfred Hitchcock’s movie Vertigo. In
terms of the camera model, two things occur simultaneously during a dolly zoom sequence: the camera moves
along the z-axis, and the focal distance of the camera changes. The distance moved and the change of focal
length are carefully chosen so that the projection of objects at a predefined distance remain at the same image
position. Objects at all other distances move relative to one another. A photographer wants to capture two
images of a scene captured at either end of a dolly zoom, such that the image positions of points in the world at
a distance of α cm relative to the camera that took the first image remain the same. The first image is captured
with a focal length of β cm. To capture the second image, the camera was moved γ cm along the z-axis in the
negative direction. What focal length should be used to capture the second image to successfully perform the
dolly zoom. Show all work.
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11. [2 points] Is a 5 × 5 filter with values all set to one separable? If yes, provide the separable filter.
12. [2 points] Explain whether convolving an image with a smoothing filter and then a Prewitt filter is equivalent
to first convolving the image by the Prewitt filter and then convolving by the same smoothing filter.
13. [5 points] You are given an (greyscale) image and tasked to generate K images (e.g., 535), where each image is
the output of the initial image convolved with a derivative of Gaussian filter rotated at a particular angle. Explain
how you would efficiently produce the K output images.